Problem: Express your answer as a mixed number simplified to lowest terms. $12\dfrac{1}{5}-7\dfrac{3}{7} = {?}$
Answer: Find a common denominator for the fractions: $= {12\dfrac{7}{35}}-{7\dfrac{15}{35}}$ Convert ${12\dfrac{7}{35}}$ to ${11 + \dfrac{35}{35} + \dfrac{7}{35}}$ So the problem becomes: ${11\dfrac{42}{35}}-{7\dfrac{15}{35}}$ Separate the whole numbers from the fractional parts: $= {11} + {\dfrac{42}{35}} - {7} - {\dfrac{15}{35}}$ Bring the whole numbers together and the fractions together: $= {11} - {7} + {\dfrac{42}{35}} - {\dfrac{15}{35}}$ Subtract the whole numbers: $=4 + {\dfrac{42}{35}} - {\dfrac{15}{35}}$ Subtract the fractions: $= 4+\dfrac{27}{35}$ Combine the whole and fractional parts into a mixed number: $= 4\dfrac{27}{35}$